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*> \brief \b DPST01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
* PIV, RWORK, RESID, RANK )
*
* .. Scalar Arguments ..
* DOUBLE PRECISION RESID
* INTEGER LDA, LDAFAC, LDPERM, N, RANK
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ),
* $ PERM( LDPERM, * ), RWORK( * )
* INTEGER PIV( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DPST01 reconstructs a symmetric positive semidefinite matrix A
*> from its L or U factors and the permutation matrix P and computes
*> the residual
*> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
*> norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> symmetric matrix A is stored:
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> The original symmetric matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N)
*> \endverbatim
*>
*> \param[in] AFAC
*> \verbatim
*> AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N)
*> The factor L or U from the L*L' or U'*U
*> factorization of A.
*> \endverbatim
*>
*> \param[in] LDAFAC
*> \verbatim
*> LDAFAC is INTEGER
*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
*> \endverbatim
*>
*> \param[out] PERM
*> \verbatim
*> PERM is DOUBLE PRECISION array, dimension (LDPERM,N)
*> Overwritten with the reconstructed matrix, and then with the
*> difference P*L*L'*P' - A (or P*U'*U*P' - A)
*> \endverbatim
*>
*> \param[in] LDPERM
*> \verbatim
*> LDPERM is INTEGER
*> The leading dimension of the array PERM.
*> LDAPERM >= max(1,N).
*> \endverbatim
*>
*> \param[in] PIV
*> \verbatim
*> PIV is INTEGER array, dimension (N)
*> PIV is such that the nonzero entries are
*> P( PIV( K ), K ) = 1.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
*>
*> \param[in] RANK
*> \verbatim
*> RANK is INTEGER
*> number of nonzero singular values of A.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
$ PIV, RWORK, RESID, RANK )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
DOUBLE PRECISION RESID
INTEGER LDA, LDAFAC, LDPERM, N, RANK
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ),
$ PERM( LDPERM, * ), RWORK( * )
INTEGER PIV( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION ANORM, EPS, T
INTEGER I, J, K
* ..
* .. External Functions ..
DOUBLE PRECISION DDOT, DLAMCH, DLANSY
LOGICAL LSAME
EXTERNAL DDOT, DLAMCH, DLANSY, LSAME
* ..
* .. External Subroutines ..
EXTERNAL DSCAL, DSYR, DTRMV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute the product U'*U, overwriting U.
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
IF( RANK.LT.N ) THEN
DO 110 J = RANK + 1, N
DO 100 I = RANK + 1, J
AFAC( I, J ) = ZERO
100 CONTINUE
110 CONTINUE
END IF
*
DO 120 K = N, 1, -1
*
* Compute the (K,K) element of the result.
*
T = DDOT( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 )
AFAC( K, K ) = T
*
* Compute the rest of column K.
*
CALL DTRMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC,
$ LDAFAC, AFAC( 1, K ), 1 )
*
120 CONTINUE
*
* Compute the product L*L', overwriting L.
*
ELSE
*
IF( RANK.LT.N ) THEN
DO 140 J = RANK + 1, N
DO 130 I = J, N
AFAC( I, J ) = ZERO
130 CONTINUE
140 CONTINUE
END IF
*
DO 150 K = N, 1, -1
* Add a multiple of column K of the factor L to each of
* columns K+1 through N.
*
IF( K+1.LE.N )
$ CALL DSYR( 'Lower', N-K, ONE, AFAC( K+1, K ), 1,
$ AFAC( K+1, K+1 ), LDAFAC )
*
* Scale column K by the diagonal element.
*
T = AFAC( K, K )
CALL DSCAL( N-K+1, T, AFAC( K, K ), 1 )
150 CONTINUE
*
END IF
*
* Form P*L*L'*P' or P*U'*U*P'
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
DO 170 J = 1, N
DO 160 I = 1, N
IF( PIV( I ).LE.PIV( J ) ) THEN
IF( I.LE.J ) THEN
PERM( PIV( I ), PIV( J ) ) = AFAC( I, J )
ELSE
PERM( PIV( I ), PIV( J ) ) = AFAC( J, I )
END IF
END IF
160 CONTINUE
170 CONTINUE
*
*
ELSE
*
DO 190 J = 1, N
DO 180 I = 1, N
IF( PIV( I ).GE.PIV( J ) ) THEN
IF( I.GE.J ) THEN
PERM( PIV( I ), PIV( J ) ) = AFAC( I, J )
ELSE
PERM( PIV( I ), PIV( J ) ) = AFAC( J, I )
END IF
END IF
180 CONTINUE
190 CONTINUE
*
END IF
*
* Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A).
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 210 J = 1, N
DO 200 I = 1, J
PERM( I, J ) = PERM( I, J ) - A( I, J )
200 CONTINUE
210 CONTINUE
ELSE
DO 230 J = 1, N
DO 220 I = J, N
PERM( I, J ) = PERM( I, J ) - A( I, J )
220 CONTINUE
230 CONTINUE
END IF
*
* Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or
* ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ).
*
RESID = DLANSY( '1', UPLO, N, PERM, LDAFAC, RWORK )
*
RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
*
RETURN
*
* End of DPST01
*
END
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